de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 2^{sin^2(1/3 x)}sin(2/3 x)

Lösung

\int 2^{s i n^{2} (\frac{1}{3} x)} sin (\frac{2}{3} x) d x

Lösung

\frac{3 \cdot 2 ^{s i n^{2} (\frac{x}{3})}}{ln ( 2 )} + C

Schritte zur Lösung

\int 2^{s i n^{2} (\frac{1}{3} x)} sin (\frac{2}{3} x) d x

Wende U-Substitution an

= \int 3 \cdot 2^{s i n^{2} (u)} sin (2 u) d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int 2^{s i n^{2} (u)} sin (2 u) d u

Wende U-Substitution an

= 3 \cdot \int 2^{v} d v

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 3 \cdot \frac{2 ^{v}}{ln ( 2 )}

Ersetze zurück

= 3 \cdot \frac{2 ^{s i n^{2} (\frac{1}{3} x)}}{ln ( 2 )}

Vereinfache

3 \cdot \frac{2 ^{s i n^{2} (\frac{1}{3} x)}}{ln ( 2 )} : \frac{3 \cdot 2 ^{s i n^{2} (\frac{x}{3})}}{ln ( 2 )}

= \frac{3 \cdot 2 ^{s i n^{2} (\frac{x}{3})}}{ln ( 2 )}

Füge eine Konstante zur Lösung hinzu

= \frac{3 \cdot 2 ^{s i n^{2} (\frac{x}{3})}}{ln ( 2 )} + C

Graph

Beliebte Beispiele

taylor 1/(x^2),-1

t a y l or \frac{1}{x ^{2}}, - 1

derivative of 7/(sqrt(x^4+3))

\frac{d}{d x} (\frac{7}{x ^{4} + 3})

limit as x approaches pi/4 of (tan(x))^{tan(2x)}

x \to \frac{π}{4} lim ((tan (x))^{t a n (2 x)})

limit as x approaches 5+of ln(x^2-25)

x \to 5 + lim (ln (x^{2} - 25))

derivative y=xsqrt(16-x^2)

d er i v a t i v e y = x 16 - x^{2}